Spectrograph



H. EWALD Oct. 30, 1962 SPECTROGRAPH 5 Sheets-Sheet 1 Filed Feb. 29, 1960 INVENTOR -HE/NZ E WALD ATTORNEYS M u M y .mfl w 3am m w. drw Y W: m B 8 W 2 H. EWALD SPECTROGRAPH Oct. 30, 1962 3 Sheets-Sheet 2 Filed Feb. 29, 1960 E Mmh 0 31m Q um w ufimcmuE 53a Q EQ INVENTOR HE/NZ EWALD 3 o v sw vian m mm QQ RQQQ 03 xomtm kou ATTORNEYS H. EWALD Oct. 30, 1962 SPECTROGRAPH 3 Sheets-Sheet 3 Filed Feb. 29, 1960 x l f INVENTOR HE/NZ EWALD Fig. 7

ATTORNEY$ United States Patent Ofifice 3,051,720 Patented Oct. 30, 1962 3,061,720 SPECTROGRAPH Heinz Ewald, 36 Clemenssu-asse, Munich, Germany Filed Feb. 29, 1960, Ser. No. 11,604 Claims. (Cl. 250--41.9)

The present invention relates to spectrographs. More in particular, the present invention relates to mass spectrographs and energy spectrographs having condensers which are corrected for image errors.

The term spectrograph as used in the present specification and claims is intended to comprehend spectrometers.

It is known that spectrographs comprise condensers which are mostly of the toroidal-shaped type which is to be understood as comprising the spherical-type condensers, but which can also be cylinder-shaped.

These condensers are electronand ion-optical focusing systems with the help of which rays of charged particles, such as electrons, elementary particles, or ions may be separated into an energy spectrum. Spherical and cylindrical condensers are special cases of the more common toroidal condensers.

The known spectrographs are unsatisfactory because of considerable image errors. Heretofo-re it has been impossible to provide condensers with a satisfactory correction of image errors. Although it has become known to provide condensers in spectrographs corrected to some extent for image errors with respect to the image error coefficient (hereinbelow designated as A of the half effective axial angle of divergence of the rays of particles passing through the spectrograph to the place of image, it has hitherto not been possible to provide special kinds of spectrographs with condensers wherein all image error coefiicients are corrected so as to become zero. Furthermore, the partial image correction of just one image error coefiicient according to the known art requires a complicated and particular configuration of the front surfaces on the entrance or the exit side or on both sides of the condensers. The front surfaces must have curvatures calculated in a determined manner.

It is therefore an object of the present invention to provide a spectrograph with condensers which are more perfectly corrected for image errors than any of the known spectrographs.

It is another object of the present invention to provide a spectrograph with condensers which are more perfectly corrected for image errors than any of the known spectrographs, which correction obtains even where double focusing mass spectrographs having condensers with plane entrance and exit surfaces are used.

It is still another object of the present invention to provide a spectrograph with condenser-s which are more perfectly corrected for image errors than any of the known spectrographs, and which do not have any intermediate radial images in and between the fields besides the final images.

Other objects and advantages of the present invention will become apparent as the description and explanation thereof proceeds.

The objects are achieved by the invention which is based on my discovery that in the known spectrographs condensers, and particularly double curved toroidal condensers are characterized by the fact that the value R' to be presently defined, is equal to one (R',,=1). According to my invention the deficiencies of the known art are overcome by providing condensers characterized by the fact that the value R is unequal to one, and may also become negative.

The invention is illustrated in the accompanying drawings, wherein:

FIGURES 1 and 2 are schematic views of toroidal condensers for use in a spectrograph constructed according to my invention;

FIGURE 3 is a sectional view of a mass spectrograph according to my invention, with direction and velocity focusing which does not have intermediate radial images in and between the fields and for which the aberration coefiicients are equal to zero;

FIGURE 4 is a sectional view of a mass spectrograph according to my invention, with a homogeneous field and a toroidal condenser having plane entrance and exit front surfaces and for which the aberration coefiicient A is equal to Zero;

FIGURE 5 is a schematic view of a spherical condenser for use in a spectrograph constructed according to my invention;

FIGURE 6 illustrates a single condenser plate used in the spectrograph shown in FIGURE 4, and

FIGURES 7, 8 and 9 illustrate sectional views of the condenser plate of FIGURE 6 and respectively taken at lines 7, 8, and 9 therein.

The following considerations, with reference to FIG- URES 1 and 2, will more fully explain the novel feature of my invention and the considerable advance over the art.

The electrodes of a toroidal condenser as shown in FIGURES 1 and 2 for example, have a common rotational axis, e.g. in FIGURE 1 the z-axis of an r, 5, z-system of cylinder coordinates, and a common plane of symmetry, as in FIGURE 1 the plane z=0. Their radial and axial main radii of curvature in the points of the circle of intersection with the plane of symmetry =0 may be r,,, r and R,,, R respectively. The radial and axial main circles of curvature are falling in the plane of symmetry and vertical to it in planes going through the z-axis, respectively. The centers of these curvatures coincide with the origin of thecoordinate system or they are located in the plane z=0 on the circles r=r,,-R and r=r --R respectively.

The section of a circle r=a (r a r z=0 located in the plane of symmetry between the electrodes together with its straight prolongations outside of the sector field may be designated as mean orbit. Orbits of charged particles progressing in the neighborhood of this mean orbit can be calculated with formulas generally known in the art.

The potential surface between the two electrodes extending through the mean orbit has the radial radius of curvature a in the points of the mean orbit; its axial radius of curvature in these points is indicated by R (see FIGURE 2). A neighboring surface of equipotential may have the axial radius of curvature R in the points of its circle of intersection with the symmetry plane 1:0. For points of the symmetry plane the derivative indicates the amount of the change of the axial radius of curvature R of the surfaces of equipotential when proceeding from a point of the mean orbit in radial r-direction to a neighboring point R and R can be calculated as functions of r a r R R and vice versa R and R can be calculated as functions of r,,, a b, e e- This formula is given by Formulas 4, 2 and 3 in my paper in Zeitschrift fiir Naturforschung (ZfN), vol. 14a, page 198, referred to below wherein r may be either r or r for the calculation of either R or R It will be understood from the formulas given in the various papers referred to below, which formulas have been made part of this specification, that this R is one of the variables to be selected in order to verify the equations for the error coefficients A A A and A As stated above this R is to be unequal to unity which is a condition found by me to render at least one of these coefiicients substantially zero in the types of apparatus discussed below. This is independent of the particular meaning of R,,. For explanatory reasons, however, it is believed to be readily apparent, that R' =l has also the following geometrical meaning: As it can be seen from FIG. 1, the radial radii 11 and r have a common origin. If the axial radii R and R had also common origin, then dR/dr would necessarily be unity, because in this'case the R of an eqnipotential surface would vary as does r taken in the direction of r; thus dR/dr= 1 would necessarily follow therefrom. Accordingly, the discovery is that dR/dr%l as a condition to render the error coefiicients zero, is equivalent to the condition that the origin of R be unequal to the origin of R in case r and r have a common origin.

The first order focusing properties (radial and axial focus lengths and image distances of the usually astigmatic focusing) of an energy spectrograph consisting of one or several toroidal condensers, as well as such properties of combinations of such condensers with magnetic fields to mass spectrographs are mainly dependent of the values of a and R and of the mean angle or angles of deflection in the condenser or in the condensers, respectively. They are not dependent of the value or the values, respectively, of R' but the second order focusing properties, especially the image errors at the points of the images are also dependent of the value or the values, respectively, of R,,.

When imaging an object point located on the mean orbit on the object side, e.-g. a point of the entrance slit of the spectrograph, into a radial focusing line located on the mean orbit on the image side (or, in the case of the so-called stigmatic focusing into an image point located on the mean orbit) by using particle rays progressing in the neighborhood of the mean orbit, the radial image errors are determined by the general formula In this formula on and a, are the half effective radial and axial angles of divergence of the rays passing through the spectrograph to the place of the image; 1 represents the half maximum relative difference of the kinetic energies of the rays passing through the spectrograph to the place of the image. a, d 1; are small compared to 1. There is another way of writing the image coefiicients, which is given in ZfN, vol. 12a, page 538, particularly on page 539, Formula 8, thereof wherein a, and a' are the same as a and given above but wherein B is half the maximum relative difference of the velocities of rays passing through the spectrograph at the place of the image (see L.c., page 538 supra). It is apparent, that ,8 and 1 are interrelated by constant factors. It is further apparent, the 1 :0 then, of course, is also A =0 etc. and vice versa. The coeflicients A to A are functions of the geometrical data of the fields and their combinations, i.e. of the radii of curvature of the mean orbits, of the surfaces of the electrodes, of the field boundaries, of the directions of the field boundaries, the relative arrangements and distances of the fields and the entrance slits, of the mean angles of deflection 4 in the fields and also of the values of R of the condensers.

According to the present invention, the condensers are so constructed, that the values R are unequal to 1 and may also be negative. It is thus possible to construct mass spectrographs corrected for image errors with which do not have any intermediate radial images in and between the fields besides the final images. It is furthermore possible to construct so-called double focusing mass spectrographs which are corrected for the radial angular aberration of axial origin (A =O) and have plane entrance and exit surfaces of the condensers, while the coefiicients A A A may be unequal to zero. And it is also possible to construct energy spectrographs which are corrected for angular aberration with A =A =0.

It is, of course, also possible to bring the coefficient A to zero in a known manner, specifically by providing the front surfaces on the entrance or the exit side or on both sides of the condensers with curvatures which are symmetrical to the plane z=O the needed radii of curvature q of which can be calculated in a manner known in the art.

On the basis of the foregoing explanation the invention will next be described with reference to two examples of spectrographs with condensers according to the invention illustrated in FIGURES 3 and 4 of the accompanying drawings.

The first example illustrated in FIGURE 3 relates to a mass spectrograph with direction and velocity focusing which does not have intermediate radial images in and between the fields and for which the aberration coefficients A A A A are equal to zero. FIGS. 6 to 9 illustrate a toroidal condenser plate used for this example defining a straight entrance but a curved (curvature q)-exit.

A schematic section through the apparatus within the symmetry plane 1:0 is shown in FIGURE 3. In this figure the values and a /R =1.36 are given arbitrarily and vertical entrance of the mean orbit into the magnetic field (e'=[)) and the attainment of stigmatic focusing (equal radial and axial image distances of the field combination) are assumed. The distance l of the entrance slit from the entrance limit of the electrical field shall be equal to the focal distance of the electrical field.

From the knowledge of gb l'. =g and from the Well-known first order double focusing condition follow the values =29.5, g =2.86a By making zero simultaneously the expressions for A A A given in Zeitschrift fiir Naturforschung 12a, 539 (1957) (H. Liebl and H. Ewald, The Image Errors of Double Focusing Mass Spectrographs, Equations 9, 10, 11), the values a =2.S6a d=5.37a k=O.745a R =-2.43 "are obtained.

The three equations for A A and A are:

aside of the known, i.e. arbitrarily selected and c=a /R the equations include the following abbreviations:

calculated value of R will be explained in the followr l negh lbly smal g example.

L =I% i H .H) 1) Mass spectrographs with A =A =A =0 and H f l' =g in which intermediate radial images in or between l l Z the fields are allowed would require much larger angles of Zl; H T) Sm deflection in one or in both of the fields.

2 A further example illustrated in FIGURE 4 relates K (1cos H (b to a mass spectrograph with direction and velocity focusa ing having a homogeneous magnetic field and a toroidal A: 1 1 condenser having plane entrance and exit front surfaces,

36 2( +R and for which A =O.

A schematic section through this apparatus located within the symmetry plane is given in FIGURE 4. In

this case the values R a =12 cm. R =9.6 cm. a =15 cm.

These are given by the paper referred to in the last are given arbitrarily and vertical entrance of the mean mentioned Paper (Ewald and Liebl Z. Naturforsch, vol. orblt into the magnetlc field assumed More 12a, page 128, et seq., 1957). r,

Furthermore, it appears that these equations for A :0 c ct W A and A include: the angle 6' which is the angle 8 Vm g Re 6 between the straight mean orbit of the particles entering is assumed As follows from Zeitschrifi fur Natup the magnetic field and the normal to theentrance boundforschung 12a 539 (1957) (H. Lifibl and Ewald, The my of the magmfuc field m the entranfe pomt' (See Page Image Errors of Double Focusing Mass Spectrographs), 538 Iatlos (m/k and R and 12a, 32 1957 (H. Ewald and H. Liebl, The Image The W g of am and can be taken from Errors of the Toroidal Condenser), there is for each field d the d1S tance of exlt the condenser,and 5 combination of this kind a linear dependence between R defiectlqn System which Fnean of 5 and f which for the special values given above has the the particles therein have a radius a k 18 the radius of form the curved entrance boundary of the magnetic deflection 0 2841 system. R' 2 If one selects a arbitrarily, the three equations for amaz I a A11 A12 and A33 are linear in If one also Selects In my example R =0.229l 1s chosen for WhlCh value one of the four yet unknowns arbitrarily, the other three 7633 and also A33 are equal to Zerocan be calculated in simply solving these three equations In the first one of these Papers referred to abmfe now having three unknowns. The above mentioned fig- VOL 12a, Page 539 (1957) the formula A33 15 ures for a a, k, and R have thus been obtained. By gwen by making zero the expression of A given in Zeitschrift 1 p2 fiir Naturforschung 12a, p. 544, Equation 17 (1957) (H. Liebl and H. Ewald, Stigmatically Focusing Mass usmg me abbrevlatlons glven m the other paper Spectrographs With Double Focusing Practically of Sec- L E B (30-2) & l B H ond Order), the value q=0.642a was obtained, q be- 33- a 2H(5c2) H sin ing the radius of a cylindrical curvature of the exit sur- B face of the condenser the axis of which is located within (cos 114 8- fiq e) the symmetry plane and is vertical to the direction of c vthe mean orbit between the two fields. sin /F The computation of the needed values of the axial 2(5c2) at, c

radii of curvature R and R of the electrodes from the B=c+c (1+R' curves of intersection of the electrode surfaces with V meridian planes extending through the rotational z-axis This equation for A can be made zero, for example, with the set of values given in column 6, lines 42 and 43.

This equation is linear in R as it can be seen from the appearance of R as factor in B, appearing as factor in L33.

The manner of determining the needed axial radii of curvature of the condenser electrodes, with R and with the radial radii of curvature r and r of the electrodes being given, is described in Zeitschrift fiir Naturforschung" 11a, 156 (1956) (R. Albrecht, The Potential in Doubly Curved Condensers), and is described more explicitly in Zeitschrift fiir Naturforschung 14a, 198 (1959) (H. Ewald, Concerning the Image Error Correction of Doubly Focusing Mass Spectrographs). This formula has been given above in column 2. From r,,: 11.6 cm. and r =l2.4 cm. and the values given above follows for this example R =9.70 cm. and R =9.52 cm.

According to still a further example of an energy spectrograph, A =A =0. The spectrograph has a toroidal condenser with the values =30, a =R r =0.95a r =1.05a l =l",,=3.73a (object distance=image distance), R =1.046, R =1.()62a R =0.9Sa which has a plane entrance front surface and a cylindrically curved exit front surface of the radius of curvature q=1.67a (outwardly convex-shaped). Due to the equality of ti and R the mean surface of equipotential between the electrodes is a spherical surface but the electrodes have toroidal surfaces each having unequal main axial and radial radii of curvature. R and from this R and R and also q may be calculated from the relations A =0 and A =0. The formulas for A and A are described in Zeitschrift fiir Naturforschung 12a, 33 (1957) (H. Ewald and H. Liebl, The Image Errors of the Toroidal Condenser), where, however, instead of A and A the designations F /a and F33/Ol respectively, are employed.

There is stated that 11=( e 11-l- "e' 11) 'r thus, in this case 11= e 11+ "e 11= We use l" instead of l"r for the sake of clarity, but 1t is understood that l" in this specification is identical with l"r in the paper just referred to. This l"r =l can be calculated. Formula 36 in ZfN, vol. 12a, page 33.

The abbreviations are given in the same paper L c, H, and A are the same abbreviations as given explicitly above. Using a =R and l' zl", we obtain for R,, the relation and from this with =30, R =1.046.

However, in the expression for F We have to insert L i-I from Zeitschrift fiir Naturforschung" 12a, 544 (1957) (H. Liebl. and H. Ewald, Mass Spectrographs Practically With Second Order Double Focusing). Using R' =l.046, q is calculated from the condition F =0.

It will be noted that instead of toroidal condensers toms-like condensers may be used provided that the axial are symmetrical to the plane z=0.

Mass and energy spectrometers and spectrographs corrected for image errors according to my invention enable the realization of higher intensities and accuracies in measuring ion abundances, masses and energies. They will be used with great advantage for physical, chemical, medical, geological, and other problems.

It will be understood that this invention is susceptible to modification in order to adapt it to different usages and conditions, and, accordingly, it is desired to comprehend such modifications within this invention as may fall within the scope of the appended claims.

What I claim is:

1. A mass spectrograph having direction and velocity focusing means, comprising; a toroidal condenser defining a mean angle of deflection a magnetic deflection system disposed in the path of particles leaving said condenser, said condenser and said deflection system causing an image error defined by the sum of with a, and 0/ being radial and axial angles, respectively, of a particle path with respect to said mean orbit and said 9 being half the maximum relative difference of the velocities of rays passing through said spectrograph at the place of the image thereof, wherein A A and A are determined by the following variable dimensions: being the mean angle of deflection in said magnetic deflection system; c, being the angle between the straight mean orbit behind said condenser and the normal to the entrance boundary; a being the radius of the mean orbit of particles in said magnetic deflection system; a being the radial radius of the mean orbit of particles in said condenser; R being the axial radius of equipotential surface through said mean orbit in said condenser; a, being the distance between said condenser and said magnetic deflection system; l' being equal to the focal distance of said condenser; It, being the radius of the entrance boundary of the magnetic field of said magnetic system; R being the derivative of axial radius of the equipotential planes by radial direction in the plane of the mean orbit in said condenser; said variables being selected under simultaneous condition of A A A being substantially zero, with R being unequal to unity, and wherein the axial radii R R for said condenser are determined by the equation wherein r may be any of the r,,, r for determination of R and R respectively.

2. Energy spectrograph comprising; a particle entrance slit; a toroidal condenser having an entrance front surface and an exit, said entrance front surface being disposed at a distance l from said particle entrance slit; said condenser focusing said particles at a distance 1",, from said exit; said condenser having a radial angle of (p, of deflection, radial radii of the condenser plates r and r axial radii thereof, R and R and defining a mean particle orbit of radial radius (1 along the equipotential surface having axial radius R the ratio a /R being designated 0, said condenser being defined by the equations:

a6 %a H-V2c e under conditions of R unequal to unity.

4. In a spectrograph, a toroidal condenser including two toroidally shaped condenser plates in which r and r are respectively predetermined radial radii of the said plates, a and R are the radial radius and the axial radius, respectively, of the mean particle orbit along an equipotential surface between said plates, axial radii R and R of said plates being determined by the equations:

with R',, being unequal to unity.

3. Mass spectrograph comprising; a particle entrance slit; a magnetic deflection system defining a mean angle of deflection p of radius a having a curved entrance boundary of radius k whereby an angle 6' is defined between the mean particle orbit and the normal to said entrance boundary at the place of entrance; a deflecting condenser having planar entrance and exit surfaces and being interposed between said particle entrance slit at a distance l' therefrom and said magnetic deflection systern at a distance d therefrom; l, and d being taken from said entrance and said exit surface, respectively, said de- 1 R, R, l2R,, fleeting condenser having a radial angle 1),, of deflection, b= b e+ 2 R radial radii of the condenser plates r and r axial radii 5 thereof, R and R and defining a mean particle orbit e of radial radius 0 along the equipotential surface having axial radius R the ratio a,,/R being designated c, said condenser being defined by the equations:

wherein R is smaller than +1.

5. In a spectrograph, a toroidal condenser including two toroidally shaped condenser plates in which r and r are respectively predetermined radial radii of the said A33: 1 plates, a and R are the radial radius and the axial radius,

2 respectively, of the mean particle orbit along an equipotential surface between said plates, axial radii R and R of said plates being determined by the equations:

+% %(cos H, nos 42 wherein R',, is unequal to +1.

BM? 1': i

2 References Cited in the file of this patent 2(5c2) 531) Ewald, Liebl and Sauermann article in pages 129-137 2 1 of Zeitschrift fiir Naturforschung, vol. 14A, 1959. 

